Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = , 70 ≤ x ≤ 110 , elsewhere (b) What is the probability that the recharge time will be less than 99 minutes? (c) What is the probability that the recharge time required is at least 81 minutes? (Round your answer to four decimal places.) (d) What is the probability that the recharge time required is between 80 and 90 minutes?